plz explain me the basic of trigonometry
Answers
Answer:
Step-by-step explanation:
Trigonometry (from Greek trigonon "triangle" + metron "measure")
Trigonometry helps us find angles and distances, and is used a lot in science, engineering, video games, and more!
Right-Angled Triangle
The triangle of most interest is the right-angled triangle. The right angle is shown by the little box in the corner:
triangle showing Opposite, Adjacent and Hypotenuse
Another angle is often labeled θ, and the three sides are then called:
Adjacent: adjacent (next to) the angle θ
Opposite: opposite the angle θ
and the longest side is the Hypotenuse
Sine, Cosine and Tangent
The main functions in trigonometry are Sine, Cosine and Tangent
They are simply one side of a right-angled triangle divided by another.
For any angle "θ":
sin=opposite/hypotenuse cos=adjacent/hypotenuse tan=opposite/adjacent
(Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.)
Example: What is the sine of 35°?
triangle 2.8 4.0 4.9 has 35 degree angle
Using this triangle (lengths are only to one decimal place):
sin(35°) = OppositeHypotenuse = 2.84.9 = 0.57...
The triangle could be larger, smaller or turned around, but that angle will always have that ratio.
Calculators have sin, cos and tan to help us, so let's see how to use them:
right angle triangle 45 degrees, hypotenuse 20
Example: How Tall is The Tree?
We can't reach the top of the tree, so we walk away and measure an angle (using a protractor) and distance (using a laser):
We know the Hypotenuse
And we want to know the Opposite
Sine is the ratio of Opposite / Hypotenuse:
sin(45°) = OppositeHypotenuse
calculator-sin-cos-tan
Get a calculator, type in "45", then the "sin" key:
sin(45°) = 0.7071...
What does the 0.7071... mean? It is the ratio of the side lengths, so the Opposite is about 0.7071 times as long as the Hypotenuse.
We can now put 0.7071... in place of sin(45°):
0.7071... = OppositeHypotenuse
And we also know the hypotenuse is 20:
0.7071... = Opposite20
To solve, first multiply both sides by 20:
20 × 0.7071... = Opposite
Finally:
Opposite = 14.14m (to 2 decimals)
When you gain more experience you can do it quickly like this:
right angle triangle 45 degrees, hypotenuse 20
Example: How Tall is The Tree?
Start with: sin(45°) = OppositeHypotenuse
We know: 0.7071... = Opposite20
Swap sides: Opposite20 = 0.7071...
Multiply both sides by 20: Opposite = 0.7071... × 20
Calculate: Opposite = 14.14 (to 2 decimals)
The tree is 14.14m tall
Try Sin Cos and Tan
Play with this for a while (move the mouse around) and get familiar with values of sine, cosine and tangent for different angles, such as 0°, 30°, 45°, 60° and 90°.
Also try 120°, 135°, 180°, 240°, 270° etc, and notice that positions can be positive or negative by the rules of Cartesian coordinates, so the sine, cosine and tangent change between positive and negative also.
So trigonometry is also about circles!
unit circle
Unit Circle
What you just played with is the Unit Circle.
It is a circle with a radius of 1 with its center at 0.
Because the radius is 1, we can directly measure sine, cosine and tangent.
Here we see the sine function being made by the unit circle:
© 2015 MathsIsFun.com v 0.81
Note: you can see the nice graphs made by sine, cosine and tangent.
Degrees and Radians
Angles can be in Degrees or Radians. Here are some examples:
Angle Degrees Radians
right angleRight Angle 90° π/2
__ Straight Angle 180° π
right angle Full Rotation 360° 2π
Repeating Pattern
Because the angle is rotating around and around the circle the Sine, Cosine and Tangent functions repeat once every full rotation (see Amplitude, Period, Phase Shift and Frequency).
cosine repeates every 360 degrees
When we want to calculate the function for an angle larger than a full rotation of 360° (2π radians) we subtract as many full rotations as needed to bring it back below 360° (2π radians):
Example: what is the cosine of 370°?
370° is greater than 360° so let us subtract 360°
370° − 360° = 10°
cos(370°) = cos(10°) = 0.985 (to 3 decimal places)
And when the angle is less than zero, just add full rotations.
Example: what is the sine of −3 radians?
−3 is less than 0 so let us add 2π radians
−3 + 2π = −3 + 6.283... = 3.283... radians
sin(−3) = sin(3.283...) = −0.141 (to 3 decimal places)
plz
